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Documents authored by Zhang, Qiuyi (Richard)

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Zhang, Qiuyi (Richard)

Document
DOI: 10.4230/LIPIcs.WABI.2018.8
New Absolute Fast Converging Phylogeny Estimation Methods with Improved Scalability and Accuracy

Authors: Qiuyi (Richard) Zhang, Satish Rao, and Tandy Warnow

Published in: LIPIcs, Volume 113, 18th International Workshop on Algorithms in Bioinformatics (WABI 2018)

Abstract
Absolute fast converging (AFC) phylogeny estimation methods are ones that have been proven to recover the true tree with high probability given sequences whose lengths are polynomial in the number of number of leaves in the tree (once the shortest and longest branch lengths are fixed). While there has been a large literature on AFC methods, the best in terms of empirical performance was DCM_NJ, published in SODA 2001. The main empirical advantage of DCM_NJ over other AFC methods is its use of neighbor joining (NJ) to construct trees on smaller taxon subsets, which are then combined into a tree on the full set of species using a supertree method; in contrast, the other AFC methods in essence depend on quartet trees that are computed independently of each other, which reduces accuracy compared to neighbor joining. However, DCM_NJ is unlikely to scale to large datasets due to its reliance on supertree methods, as no current supertree methods are able to scale to large datasets with high accuracy. In this study we present a new approach to large-scale phylogeny estimation that shares some of the features of DCM_NJ but bypasses the use of supertree methods. We prove that this new approach is AFC and uses polynomial time. Furthermore, we describe variations on this basic approach that can be used with leaf-disjoint constraint trees (computed using methods such as maximum likelihood) to produce other AFC methods that are likely to provide even better accuracy. Thus, we present a new generalizable technique for large-scale tree estimation that is designed to improve scalability for phylogeny estimation methods to ultra-large datasets, and that can be used in a variety of settings (including tree estimation from unaligned sequences, and species tree estimation from gene trees).
Cite as

Qiuyi (Richard) Zhang, Satish Rao, and Tandy Warnow. New Absolute Fast Converging Phylogeny Estimation Methods with Improved Scalability and Accuracy. In 18th International Workshop on Algorithms in Bioinformatics (WABI 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 113, pp. 8:1-8:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{zhang_et_al:LIPIcs.WABI.2018.8,
  author =	{Zhang, Qiuyi (Richard) and Rao, Satish and Warnow, Tandy},
  title =	{{New Absolute Fast Converging Phylogeny Estimation Methods with Improved Scalability and Accuracy}},
  booktitle =	{18th International Workshop on Algorithms in Bioinformatics (WABI 2018)},
  pages =	{8:1--8:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-082-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{113},
  editor =	{Parida, Laxmi and Ukkonen, Esko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2018.8},
  URN =		{urn:nbn:de:0030-drops-93108},
  doi =		{10.4230/LIPIcs.WABI.2018.8},
  annote =	{Keywords: phylogeny estimation, short quartets, sample complexity, absolute fast converging methods, neighbor joining, maximum likelihood}
}

Zhang, Qiuyi

Document
DOI: 10.4230/LIPIcs.ITCS.2018.22
Convergence Results for Neural Networks via Electrodynamics

Authors: Rina Panigrahy, Ali Rahimi, Sushant Sachdeva, and Qiuyi Zhang

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

Abstract
We study whether a depth two neural network can learn another depth two network using gradient descent. Assuming a linear output node, we show that the question of whether gradient descent converges to the target function is equivalent to the following question in electrodynamics: Given k fixed protons in R^d, and k electrons, each moving due to the attractive force from the protons and repulsive force from the remaining electrons, whether at equilibrium all the electrons will be matched up with the protons, up to a permutation. Under the standard electrical force, this follows from the classic Earnshaw's theorem. In our setting, the force is determined by the activation function and the input distribution. Building on this equivalence, we prove the existence of an activation function such that gradient descent learns at least one of the hidden nodes in the target network. Iterating, we show that gradient descent can be used to learn the entire network one node at a time.
Cite as

Rina Panigrahy, Ali Rahimi, Sushant Sachdeva, and Qiuyi Zhang. Convergence Results for Neural Networks via Electrodynamics. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 22:1-22:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{panigrahy_et_al:LIPIcs.ITCS.2018.22,
  author =	{Panigrahy, Rina and Rahimi, Ali and Sachdeva, Sushant and Zhang, Qiuyi},
  title =	{{Convergence Results for Neural Networks via Electrodynamics}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{22:1--22:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.22},
  URN =		{urn:nbn:de:0030-drops-83521},
  doi =		{10.4230/LIPIcs.ITCS.2018.22},
  annote =	{Keywords: Deep Learning, Learning Theory, Non-convex Optimization}
}
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